OMG... Touching the case when the PC isn't plugged in is literally just discharging your static variance right into the freaking PC.
The advice for touching the case now and again to prevent static shock depends on the PSU being plugged into a grounded outlet, and attached to the case.
The strap doesn't prevent static discharge - it just makes you in line with the case, which works to prevent static discharge whether it is plugged in or not. However, if you touch say a component on your desk, while strapped to your case which is not plugged in - you CAN still discharge.
So even with the straps they are only 100% effective if the case is plugged in. Computer cases aren't so large like cars or buildings where the are self grounding due to their mass.
Leaving it plugged in, unplugging it - either way the chances of anything happening to it are extremely small. I don't know where you guys live that lightning strikes or power surges are a problem - here in the US we have a number of codes and structures in place to prevent these sorts of things.
I always leave my PC plugged in and on, with a port forward for each rig - what if i need to remote access my PC and get some files or update the torrents, etc? What if we need an impromptu vent server for the nieces and nephews while on vacation? Leave it on and plugged in is what i'd do.